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根据样本量和极差估计样本方差。

Estimating the sample variance from the sample size and range.

作者信息

Rychtář Jan, T Taylor Dewey

机构信息

Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, Virginia, USA.

出版信息

Stat Med. 2020 Dec 30;39(30):4667-4686. doi: 10.1002/sim.8747. Epub 2020 Sep 15.

Abstract

For meta-analysis studies and systematic reviews, it is important to pool the data from a set of similar clinical trials. To pool the data, one needs to know their SD. Many trial reports, however, contain only the median, the minimum and maximum values, and the sample size. It is therefore important to be able to estimate the SD S from the sample size n and range r. For small n ≤ 100, we improve existing estimators of r/S, the "divisor," denoted by . This in turn yields improved estimators of the SD in the form on simulated as well as real datasets. We provide numerical values of the proposed estimator as well as approximation by a simple formula . Furthermore, for large n, we provide estimators of the divisor for the normal, exponential, and other bounded and unbounded distributions.

摘要

对于荟萃分析研究和系统评价而言,汇集一组相似临床试验的数据非常重要。为了汇集数据,需要知道其标准差(SD)。然而,许多试验报告仅包含中位数、最小值和最大值以及样本量。因此,能够根据样本量(n)和极差(r)来估计标准差(S)很重要。对于小样本量(n\leq100),我们改进了现有的极差与标准差之比(“除数”)(r/S)的估计量,用(\cdots)表示。这反过来又在模拟数据集和真实数据集上得到了形式为(\cdots)的标准差改进估计量。我们给出了所提出估计量的数值以及通过一个简单公式(\cdots)的近似值。此外,对于大样本量(n),我们给出了正态分布、指数分布以及其他有界和无界分布的除数(\cdots)的估计量(\cdots) 。

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